Roshan and Shojai [1]} analyzed that
\(\mathrm {EMSG}\)  gravity may describe the exact sequence of cosmic
phases and can prevent the existence of early-times singularities
with a particular functional form defined as \(f(\mathbf {R},\mathbf {T}^{2})=\mathbf {R}+\eta \mathbf {T}^{2}\) , where \(\eta \) 
denotes a constant. Akarsu et al. [2]} proposed an ETG by adopting the addition of the term \(f(R,T_{\alpha \beta }T^{\alpha \beta })\)  in the usual action function. After taking a particular case of \(f(R,T_{\alpha \beta }T^{\alpha \beta })\)  theory, they presented a few viable bounds in order to discuss late-time accelerated cosmic expansion. Board and Barrow [3]}
explored the cosmological effects by incorporating the non-linear
term \((T_{\alpha \beta }T^{\alpha \beta })^{n}\)  to the matter Lagrangian
which is the extension of \(\mathrm {EMSG}\)  gravity, wherein the model
is defined by \(f(\mathbf {R}, \mathbf {T}^{2})=\mathbf {R}+\eta (\mathbf {T}^{2})^{n}\) , where \(n\)  and \(\eta \)  are constants. Notice that [2]} and [3]} consider exactly the same gravity model.
These two papers were appeared on arXiv and published almost simultaneously.
Against
the background of \(\mathrm {EMSG}\)  cosmology, Moraes and Sahoo
[6]} examined the non-exotic matter wormholes,
and Akarsu et al. [7]} investigated
feasible constraints form the compact objects like neutron stars.
Nari and Roshan [8]} calculated two different type
of cosmological solutions for compact stars, one of them corresponds
to pressureless star while other exact solution represents a star
with constant effective density, within the bounds of
\(\mathrm {EMSG}\) . Bahamonde et al.
[9]} inspected the cosmic dynamics
mediating from the \(\mathrm {EMSG}\)  theory of gravitation via minimal
as well as non-minimal coupling models. These models can explain the
present cosmic evolution and the emergence of accelerated cosmic
expansion. Akarsu et al. [10]}
proposed a scale independent model of \(\mathrm {EMSG}\)  theory that
permits various types of gravitational couplings and also introduced
a generalized form of \(\Lambda \mathrm {CDM}\)  cosmic model within this
new theory. In addition, recent recent research
[11]}, [12]} explain
various cosmological consequences emerging from the \(\mathrm {EMSG}\) .
